What is the speed of a river?

Question

A paddle boat can move at a speed of 12 km/h in still water. The boat is paddled 6 km downstream in a river in the same time it takes to go 3 km upstream. What is the speed of the river?

Answer 1

12 + c = speed of the boat downstream

12 - c = speed of the boat upstream

 

r · t = d

t = d/r

 

for downstream

 t = 6/(12 + c)

 

for upstream

t = 3/(12 - c)

 

times are equal

6/(12 + c) = 3/(12 - c)

6(12 - c) = 3(12 + c)

72 - 6c = 36 + 3c

36 = 9c

4 = c

 

The current is 4 mph.